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From |
Richard Williams <Richard.A.Williams.5@ND.edu> |

To |
statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Chi-square test for Categorical Data Analysis |

Date |
Wed, 19 Sep 2007 23:58:48 -0500 |

At 01:05 PM 9/19/2007, Austin Nichols wrote:

I hate ordinal variables like this - and I think it is even worse when they are independent rather than dependent variables. You don't like to treat them as continuous, nor do you like to create a bunch of dummies. Mid-point scoring is popular and easy but still problematic.David Radwin <radwin@berkeley.edu>: Any technique may lead you astray, but the technique you describe is, I suspect, demonstrably inferior to others. The reference you cite applies only to estimating the mean or median of an open-ended category with a Pareto distribution, and its abstract says that "the choice of method and the selection of a mean or median estimator for the open-ended category midpoint have substantial effects on analyses in which income is the dependent variable." The -intreg- approach proposed by Maarten relies on some shaky assumptions, but I expect it is far preferable to imputing the midpoint of intervals and testing for a difference in means as if you have real data.

One possibility is to consider scoring methods. See section 6.2 of Powers & Xie:

http://www.stata.com/bookstore/smcda.html

When the ordinal var is independent, Long & Freese outline how to test whether it can be treated as continuous. See especially pp. 421-422 of

http://www.stata.com/bookstore/regmodcdvs.html

In principle, I think the intreg command sounds great. I wish Long and Freese discussed it in their book. What worries me are the "shaky assumptions" Austin mentions, especially since I don't have a very good feel for how often these assumptions are likely to be violated and what the consequences are. My own mini-mini discussion of intreg can be found at

http://www.nd.edu/~rwilliam/stats3/intreg3.pdf

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Richard Williams, Notre Dame Dept of Sociology

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**References**:**Re: st: Chi-square test for Categorical Data Analysis***From:*"Austin Nichols" <austinnichols@gmail.com>

**Re: st: Chi-square test for Categorical Data Analysis***From:*"Austin Nichols" <austinnichols@gmail.com>

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